try to test it
the battery gives u around 12 V
after starting the car it gives more than 13 V - 14 V
try to test it when u have the problem see how mane volts it gives u ?
and I heard some one had the same problem u have with lumina 1996
it was a wire under the motor gets hot so stop working,,,,,,!

 

so its no longer dieing on you or you havent had it running long enough to know? i was going to say it sure sounds like a ignition control modual.